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Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.
Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.
Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?